Properties of free entropy related to polar decomposition

Fumio Hiai, D. Petz

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The free entropies χ̂(a1,...,aN) of non-selfadjoint random variables and χu(u1,...,uN) of unitary random variables are introduced and discussed by the methods of Voiculescu's free analysis. The additivity χu(u1,...,uN) = ∑i χu(ui) is shown to be equivalent to freeness. The relation among χ̂, χu and χ is investigate in the case when ai = uihi is the polar decomposition. The subadditivity χ̂(a1,...,aN) <χu(u1,...,uN) + χ(h21,...,h2N) + constant is proven and applications to some maximization problems for χ̂ are given.

Original languageEnglish
Pages (from-to)421-444
Number of pages24
JournalCommunications in Mathematical Physics
Volume202
Issue number2
Publication statusPublished - Apr 1999

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Free Entropy
Polar decomposition
random variables
Random variable
entropy
Subadditivity
decomposition
Additivity

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Properties of free entropy related to polar decomposition. / Hiai, Fumio; Petz, D.

In: Communications in Mathematical Physics, Vol. 202, No. 2, 04.1999, p. 421-444.

Research output: Contribution to journalArticle

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